I thought Bhaisajyaguru belonged to the eastern Buddha Land Abhirati, traditionally.

Abhirati is the Pure Land of Akshobya Buddha, who is one of the 5 Dhyani Buddhas & used to be popular in East Asian Mahayana until the fame of Bhaisajyaguru Buddha and His Pure Lapis Lazuli Land took over but still highly regarded. One example of mention on Akshobya Buddha and Abhirati is the Vimalakirtinirdesa Sutra. In each direction, there are Pure Lands of various Buddhas and Bodhisattvas, so Akshobya Buddha's Abhirati is not the sole one.

Son wrote:I thought Bhaisajyaguru belonged to the eastern Buddha Land Abhirati, traditionally.

What would be the correct way to prounounce the name?.. Bha-aisha-jya-guru

Bhaiṣajyaguru (भैषज्यगुरु) is pronounced Bhai-shaj-ya-gu-ru, that is, if it is pronounced as it is written. It might be pronounced Bhai-sha-ja-gu-ru or Bhai-shag-ya-gu-ru, depending on who you ask. No matter what, the 'ai' is long, and the 'a' and 'u' are short.